let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

The goal of this article is to construct a crossed module representing the cocycle 〈[, ], 〉 generating H(g; C) for a simple complex Lie algebra g.

The construction of a Lyapunov function characterizing the pullback attraction of a cocycle attractor of a nonautonomous discrete time dynamical system involving Lipschitz continuous mappings is presented.

We consider Hölder continuous fiber bunched GL(d,R)-valued cocycles over an Anosov diffeomorphism. We show that two such cocycles are Hölder continuously cohomologous if they have equal periodic data, and prove a result for cocycles with conjugate periodic data. We obtain a corollary for cohomology between any constant cocycle and its small perturbation. The fiber bunching condition means that ...